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[Перевод] Как работают трансформеры: разбираем математику

fc1a4c81f273b8ed87c1861e5aa8c210.png

В этом посте я представлю подробный пример математики, используемой внутри модели трансформера, чтобы вы получили хорошее представление о работе модели. Чтобы пост был понятным, я многое упрощу. Мы будем выполнять довольно много вычислений вручную, поэтому снизим размерность модели. Например, вместо эмбеддингов из 512 значений мы используем эмбеддинги из 4 значений. Это позволит упростить понимание вычислений. Мы используем произвольные векторы и матрицы, но при желании вы можете выбрать собственные значения.

Как вы увидите, математика модели не так уж сложна. Сложность возникает из-за количества этапов и количества параметров. Перед прочтением этой статьи я рекомендую прочитать пост Illustrated Transformer (или читать их параллельно) [перевод на Хабре]. Это отличный пост, объясняющий модель трансформера интуитивным (и наглядным!) образом, поэтому я не буду объяснять то, что уже объяснено в нём. Моя цель заключается в том, чтобы объяснить, как работает модель трансформера, а не что это такое. Если вы хотите углубиться в подробности, то изучите известную статью Attention is all you need [перевод на Хабре: первая и вторая части].

Обязательные требования

Для понимания статьи необходимы базовые знания линейной алгебры; в основном мы будем выполнять простые матричные умножения, так что специалистом быть необязательно. Кроме того, будут полезны знания основ машинного обучения и глубокого обучения.

Что рассматривается в статье?

  • Полный пример математических вычислений, происходящих в модели трансформера в процессе инференса

  • Объяснение механизмов внимания

  • Объяснение остаточных связей и нормализации слоёв

  • Код для масштабирования модели

Наша цель будет заключаться в использовании модели трансформера в качестве инструмента для перевода, чтобы мы могли передать модели входные данные и ожидать от неё генерации перевода. Например, мы можем передать «Hello World» на английском и ожидать на выходе получить «Hola Mundo» на испанском.

Давайте взглянем на пугающую диаграмму трансформера (не бойтесь, скоро вы её поймёте!):

Модель трансформера из статьи «Attention is all you need»
Модель трансформера из статьи «Attention is all you need»

Исходная модель трансформера состоит из двух частей: кодировщика (encoder) и декодера (decoder). Кодировщик занимается «пониманием» или «осознанием смысла» входного текста, а декодер выполняет генерацию выходного текста. Давайте рассмотрим кодировщик.

Кодировщик

Цель работы кодировщика заключается в генерации обогащённого эмбеддингами описания входного текста. Этот эмбеддинг отражает семантическую информацию о входном тексте и передаётся декодеру для генерации выходного текста. Кодировщик состоит из стека из N слоёв. Прежде чем переходить к слоям, нужно разобраться, как передавать слова (или токены) в модель.

Примечание

Термин «эмбеддинг» используется слишком часто. Сначала мы создадим эмбеддинг, который будет входными данными для кодировщика. Кодировщик тоже создаёт на выходе эмбеддинг (иногда называемый hidden states). Декодер тоже получает эмбеддинг! Весь смысл в том, что эмбеддинг описывает токен в виде вектора.

0. Токенизация

Модели машинного обучения могут обрабатывать числа, а не текст, так что нам нужно превратить входной текст в числа. Именно это и выполняет токенизация! Это процесс разбиения входного текста на токены, с каждым из которых связан ID. Например, мы можем разделить текст «Hello World» на два токена: «Hello» и «World». Также мы можем разбить его на символы: «H», «e», «l», «l», «o», « »,«W», «o», «r», «l», «d». Мы сами можем выбирать принцип токенизации, он зависит от данных, с которыми мы работаем.

Для токенизации по словам (разбиения текста на слова) требуется очень большой словарь (всех возможных токенов). В нём слова наподобие «dog» и «dogs» или «run» и «running» будут разными токенами. Словарь символов потребует меньшего объёма, но будет обладать меньшим смыслом (он может быть полезен в языках наподобие китайского, где каждый символ содержит больше информации).

Прогресс двинулся в сторону токенизации по подсловам. Это нечто среднее между токенизацией по словам и по символам. Мы разделяем слова на подслова. Например, слово «tokenization» можно разбить на «token» и «ization». Как принимается решение о месте разбиения слов? Это часть обучения токенизатора при помощи статистического процесса, задача которого заключается в выявлении подслов, которые лучше всего выбрать для конкретного датасета. Это детерминированный процесс (в отличие от обучения модели машинного обучения).

В этой статье я для простоты использую токенизацию по словам. Наша цель будет заключаться в переводе «Hello World» с английского на испанский. Пример «Hello World» мы разобьём на токены «Hello» и «World». Каждому токену присваивается в словаре модели ID. Например, «Hello» может быть токеном 1, а «World» — токеном 2.

1. Эмбеддинг текста

Хотя мы можем передать модели ID токенов (то есть 1 и 2), эти числа не несут никакого смысла. Нужно превратить их в векторы (список чисел). Именно это и выполняет процесс эмбеддинга! Эмбеддинги токена сопоставляют ID токена с вектором фиксированной длины, имеющим семантическое значение токенов. Это создаёт интересные свойства: схожие токены будут иметь схожий эмбеддинг (иными словами, вычисление косинусного коэффициента между двумя эмбеддингами даст нам хорошее понимание степени схожести токенов).

Стоит заметить, что отображение токена в эмбеддинг изучается моделью. Хотя мы можем использовать уже обученный эмбеддинг наподобие word2vec или GloVe, в процессе своего обучения модели трансформеров изучают эти эмбеддинги. Это большое преимущество, поскольку модель может изучить наилучшее описание токенов для поставленной перед ней задачи. Например, модель может научиться тому, что «dog» и «dogs» должны иметь схожие эмбеддинги.

Все эмбеддинги в одной модели имеют одинаковый размер. В трансформере из научной статьи использовался размер 512, но чтобы мы могли выполнять вычисления, снизим его размер до 4. Я назначу каждому токену случайные значения (как говорилось выше, это отображение обычно изучается моделью).

Hello -> [1,2,3,4]

World -> [2,3,4,5]

Примечание

После публикации статьи многие читатели задали вопросы о представленных выше эмбеддингах. Мне было лениво и я просто записал числа, с которыми будет удобно выполнять вычисления. На практике эти числа будут изучаться моделью. Чтобы это было понятнее, я дополнил пост.

Мы можем вычислить схожесть этих векторов при помощи косинусного коэффициента, который для представленных выше векторов будет слишком высоким. На практике вектор, скорее всего, будет выглядеть примерно так: [-0.071, 0.344, -0.12, 0.026, …, -0.008].

Мы можем представить наши входные данные в виде единой матрицы

21ac942d73e513a75f7e6435f4827fca.png

Примечание

Хотя мы и можем обрабатывать два эмбеддинга как два отдельных вектора, проще работать с ними как с единой матрицей, потому что в дальнейшем мы будем выполнять умножение матриц.

2. Позиционное кодирование

Отдельные эмбеддинги в матрице не содержат информации о позиции слов в предложении, так что нам нужна информация о позиции. Её можно создать, добавив к эмбеддингу позиционное кодирование.

Получить его можно различными способами; мы можем использовать изученный эмбеддинг или фиксированный вектор. В исходной научной статье используется фиксированный вектор, потому что авторы не увидели почти никакой разницы между двумя методиками (см. раздел 3.5 статьи). Мы тоже воспользуемся фиксированным вектором. Функции синуса и косинуса имеют волнообразный паттерн и повторяются. Благодаря использованию этих функций каждая позиция в предложении получает уникальное, но согласованное позиционное кодирование. Их повторяемость поможет модели проще изучать паттерны наподобие близости и расстояния между элементами. В статье используются следующие функции:

07739ac8ce5c811f974ff3d5150159cc.png

Смысл заключается в интерполяции между синусом и косинусом для каждого значения в эмбеддинге (для чётных индексов используется синус, для нечётных используется косинус). Давайте вычислим их для нашего примера!

Для «Hello»

  • i = 0 (чётный): PE(0,0) = sin(0 / 10000^(0 / 4)) = sin(0) = 0

  • i = 1 (нечётный): PE(0,1) = cos(0 / 10000^(2*1 / 4)) = cos(0) = 1

  • i = 2 (чётный): PE(0,2) = sin(0 / 10000^(2*2 / 4)) = sin(0) = 0

  • i = 3 (нечётный): PE(0,3) = cos(0 / 10000^(2*3 / 4)) = cos(0) = 1

Для «World»

  • i = 0 (чётный): PE(1,0) = sin(1 / 10000^(0 / 4)) = sin(1 / 10000^0) = sin(1) ≈ 0.84

  • i = 1 (нечётный): PE(1,1) = cos(1 / 10000^(2*1 / 4)) = cos(1 / 10000^0.5) ≈ cos(0.01) ≈ 0.99

  • i = 2 (чётный): PE(1,2) = sin(1 / 10000^(2*2 / 4)) = sin(1 / 10000^1) ≈ 0

  • i = 3 (нечётный): PE(1,3) = cos(1 / 10000^(2*3 / 4)) = cos(1 / 10000^1.5) ≈ 1

В итоге получаем следующее:

  • «Hello» -> [0, 1, 0, 1]

  • «World» -> [0.84, 0.99, 0, 1]

Обратите внимание, что эти кодировки имеют ту же размерность, что и исходный эмбеддинг.

Примечание

Мы используем синус и косинус, как и в исходной научной статье, но есть и другие способы реализации. В очень популярном трансформере BERT применяются обучаемые позиционные эмбеддинги.

3. Добавляем позиционное кодирование и эмбеддинг

Теперь мы добавим к эмбеддингу позиционное кодирование. Это выполняется сложением двух векторов.

«Hello» = [1,2,3,4] + [0, 1, 0, 1] = [1, 3, 3, 5]

«World» = [2,3,4,5] + [0.84, 0.99, 0, 1] = [2.84, 3.99, 4, 6]

То есть наша новая матрица, которая будет входными данными для кодировщика, выглядит так:

b3c1f5027a551dfb3e3e73cc91d26fa3.png

Если посмотреть на изображение из научной статьи, то можно увидеть, что мы только что выполнили левую нижнюю часть изображения (эмбеддинг + позиционное кодирование).

Модель трансформера из статьи «Attention is all you need»
Модель трансформера из статьи «Attention is all you need»

4. Самовнимание

4.1 Определение матриц

Теперь мы введём концепцию многоголового внимания (multi-head attention). Внимание — это механизм, позволяющий модели сосредоточиться на определённых частях входных данных. Многоголовое внимание позволяет модели совместно уделять внимание информации из различных подпространств описаний. Для этого используются множественные головы внимания. Каждая голова внимания имеет собственные матрицы K, V и Q.

Давайте в нашем примере используем две головы внимания. Для этих матриц мы применим случайные значения. Каждая матрица будет иметь размер 4x3. Благодаря этому каждая матрица будет преобразовывать четырёхмерные эмбеддинги в трёхмерные ключи (K), значения (V) и запросы (Q). Это снижает размерность механизма внимания, что помогает управлять вычислительной сложностью. Стоит отметить, что использование слишком малого размера внимания уменьшит точность модели. Давайте используем следующие значения (выбраны произвольно):

Для первой головы

6d6536a6f378872e5551e5ae957dbdf9.png

Для второй головы

ae855c0cdc319b6b83cbfe04f7b10b73.png

4.2 Вычисление ключей, запросов и значений

Для получения ключей, запросов и значений нужно умножить входные эмбеддинги на матрицы весов.

Вычисление ключей

b022aa1304298a0573f65941cb2d6acf.png

На самом деле, нам не нужно вычислять всё это вручную, это будет слишком монотонно. Давайте схитрим и воспользуемся NumPy.

Сначала определим матрицы

import numpy as np

WK1 = np.array([[1, 0, 1], [0, 1, 0], [1, 0, 1], [0, 1, 0]])
WV1 = np.array([[0, 1, 1], [1, 0, 0], [1, 0, 1], [0, 1, 0]])
WQ1 = np.array([[0, 0, 0], [1, 1, 0], [0, 0, 1], [1, 0, 0]])

WK2 = np.array([[0, 1, 1], [1, 0, 1], [1, 1, 0], [0, 1, 0]])
WV2 = np.array([[1, 0, 0], [0, 1, 1], [0, 0, 1], [1, 0, 0]])
WQ2 = np.array([[1, 0, 1], [0, 1, 0], [1, 0, 0], [0, 1, 1]])

И убедимся, что в приведённых выше вычислениях нет никаких ошибок.

embedding = np.array([[1, 3, 3, 5], [2.84, 3.99, 4, 6]])
K1 = embedding @ WK1
K1
array([[4.  , 8.  , 4.  ],
       [6.84, 9.99, 6.84]])

Отлично! Теперь давайте получим значения и запросы

Вычисление значений

V1 = embedding @ WV1
V1
array([[6.  , 6.  , 4.  ],
       [7.99, 8.84, 6.84]])

Вычисление запросов

Q1 = embedding @ WQ1
Q1
array([[8.  , 3.  , 3.  ],
       [9.99, 3.99, 4.  ]])

Давайте пока пропустим вторую голову и сосредоточимся на окончательном результате первой головы. Ко второй голове мы вернёмся позже.

4.3 Вычисление внимания

Для вычисления показателя внимания требуется пара шагов:

  1. Вычисление скалярного произведения запроса и каждого ключа

  2. Деление результата на квадратный корень размерности вектора ключа

  3. Применение функции softmax для получения весов внимания

  4. Умножение каждого вектора значения на веса внимания

4.3.1 Скалярное произведение запроса и каждого ключа

Для вычисления результата для «Hello» необходимо вычислить скалярное произведение q1 и каждого вектора ключа (k1 и k2)

9d2504e2828fd8ea6d6c94e98d42be9a.png

В мире матриц это будет равно Q1, умноженному на перестановку K1

6e4a5525d96bde952b7b76024dc842d5.png

Я могу сделать ошибку, так что давайте проверим всё это ещё раз с помощью Python

scores1 = Q1 @ K1.T
scores1
array([[ 68.    , 105.21  ],
       [ 87.88  , 135.5517]])

4.3.2 Деление на квадратный корень размерности вектора ключа

Затем мы делим показатели на квадратный корень размерности (d) ключей (в данном случае это 3, но в научной статье она была равна 64). Почему? При больших значениях d скалярное произведение растёт слишком быстро (ведь мы складываем умножение кучи чисел, что приводит к большим значениям). А большие значения — это плохо! Подробнее мы поговорим об этом чуть позже.

scores1 = scores1 / np.sqrt(3)
scores1
array([[39.2598183 , 60.74302182],
       [50.73754166, 78.26081048]])

4.3.3 Применение функции softmax

Далее используем softmax для нормализации, чтобы все они были положительны и в сумме равнялись 1.

Что такое softmax?

Softmax — это функция, получающая вектор значений и возвращающая вектор значений между 0 и 1, в котором сумма значений равна 1. Это удобный способ получения вероятностей. Функция определяется следующим образом:

e7a48588f466c4234929d03def3500f0.png

Не пугайтесь этой формулы, на самом деле она довольно проста. Допустим, у нас есть следующий вектор:

c750d84109caee4305daf1dfafe58f80.png

Softmax этого вектора будет такой:

c6c21d57fe4f33b902add6e0b6bed43f.png

Как видите, все значения положительны и в сумме дают 1.

def softmax(x):
    return np.exp(x) / np.sum(np.exp(x), axis=1, keepdims=True)


scores1 = softmax(scores1)
scores1
array([[4.67695573e-10, 1.00000000e+00],
       [1.11377182e-12, 1.00000000e+00]])

4.3.4 Умножение матрицы значений на веса внимания

Далее мы умножаем на матрицу значений

attention1 = scores1 @ V1
attention1
array([[7.99, 8.84, 6.84],
       [7.99, 8.84, 6.84]])

Давайте объединим 4.3.1, 4.3.2, 4.3.3 и 4.3.4 в одну формулу с использованием матриц (это из раздела 3.2.1 научной статьи):

a02751d90c6c85873ce9b30671a9496a.png

Да, вот и всё! Все проделанные нами вычисления можно легко свести к показанной выше формуле внимания! Давайте перенесём это в код.

def attention(x, WQ, WK, WV):
    K = x @ WK
    V = x @ WV
    Q = x @ WQ

    scores = Q @ K.T
    scores = scores / np.sqrt(3)
    scores = softmax(scores)
    scores = scores @ V
    return scores
attention(embedding, WQ1, WK1, WV1)
array([[7.99, 8.84, 6.84],
       [7.99, 8.84, 6.84]])

Мы убедились, что значения те же, что и получены выше. Давайте воспользуемся этим кодом для получения показателей внимания второй головы внимания:

attention2 = attention(embedding, WQ2, WK2, WV2)
attention2
array([[8.84, 3.99, 7.99],
       [8.84, 3.99, 7.99]])

Если вас интересует, как внимание стало одинаковым для двух эмбеддингов, то это вызвано тем, что softmax переводит показатели в 0 и 1. Смотрите:

softmax(((embedding @ WQ2) @ (embedding @ WK2).T) / np.sqrt(3))
array([[1.10613872e-14, 1.00000000e+00],
       [4.95934510e-20, 1.00000000e+00]])

Это вызвано плохой инициализацией матриц и маленьким размерам векторов. Большие различиях в показателях до применения softmax будут лишь усилены, приводя к том, что одно значение будет близко к 1, а другие к 0. На практике наши исходные значения матрицы эмбеддингов были слишком велики, что привело к высоким значениям для ключей, значений и запросов, которые при умножении становились только выше.

Помните, как мы выполняли деление на квадратный корень размерности ключей? Именно поэтому мы это и делали, в противном случае значения скалярного произведения были бы слишком большими, из-за чего получились бы большие значения после softmax. Однако в данном случае, похоже, этого не было достаточно, учитывая наши небольшие значения! В качестве быстрого хака мы можем уменьшить масштаб значений на меньшее значение, чем квадратный корень трёх. Давайте переопределим функцию внимания, уменьшив масштаб на 30. В долгой перспективе это плохое решение, но оно поможет нам получить разные значения для показателей внимания. Позже мы вернёмся к более качественному решению.

def attention(x, WQ, WK, WV):
    K = x @ WK
    V = x @ WV
    Q = x @ WQ

    scores = Q @ K.T
    scores = scores / 30  # we just changed this
    scores = softmax(scores)
    scores = scores @ V
    return scores
attention1 = attention(embedding, WQ1, WK1, WV1)
attention1
array([[7.54348784, 8.20276657, 6.20276657],
       [7.65266185, 8.35857269, 6.35857269]])
attention2 = attention(embedding, WQ2, WK2, WV2)
attention2
array([[8.45589591, 3.85610456, 7.72085664],
       [8.63740591, 3.91937741, 7.84804146]])

4.3.5 Выходные значения внимания голов

Следующий слой кодировщика ожидает на входе одну матрицу, а не две. Первым этапом будет конкатенация выходных значений двух голов (см. раздел 3.2.2 научной статьи)

attentions = np.concatenate([attention1, attention2], axis=1)
attentions
array([[7.54348784, 8.20276657, 6.20276657, 8.45589591, 3.85610456,
        7.72085664],
       [7.65266185, 8.35857269, 6.35857269, 8.63740591, 3.91937741,
        7.84804146]])

Затем мы умножаем эту конкатенированную матрицу на матрицу весов, чтобы получить окончательный результат слоя внимания. Этой матрице весов модель тоже обучается! Размерность матрицы гарантирует, что мы вернёмся к той же размерности, что была у эмбеддинга (в нашем случае 4).

# Просто произвольные значения
W = np.array(
    [
        [0.79445237, 0.1081456, 0.27411536, 0.78394531],
        [0.29081936, -0.36187258, -0.32312791, -0.48530339],
        [-0.36702934, -0.76471963, -0.88058366, -1.73713022],
        [-0.02305587, -0.64315981, -0.68306653, -1.25393866],
        [0.29077448, -0.04121674, 0.01509932, 0.13149906],
        [0.57451867, -0.08895355, 0.02190485, 0.24535932],
    ]
)
Z = attentions @ W
Z
array([[ 11.46394285, -13.18016471, -11.59340253, -17.04387829],
       [ 11.62608573, -13.47454936, -11.87126395, -17.4926367 ]])

Всё это можно объединить в изображение из The Ilustrated Transformer

Attention
Attention

5. Слой с прямой связью

5.1 Простой слой с прямой связью

После слоя самовнимания у кодировщика идёт нейронная сеть с прямой связью (feed-forward neural network, FFN). Это простая сеть с двумя линейными преобразованиями и активацией ReLU между ними. В посте The Illustrated Transformer подробностей об этом нет, так что я вкратце объясню этот слой. Цель FFN заключается в обработке и трансформировании описания, созданного механизмом внимания. Поток обычно выглядит так (см. раздел 3.3 научной статьи):

  1. Первый линейный слой: обычно он расширяет размерность входных данных. Например, если размерность входных данных равна 512, то размерность выходных данных может быть равна 2048. Это выполняется для того, чтобы позволить модели изучать более сложные функции. В нашем простом примере с размерностью 4 мы расширимся до 8.

  2. Активация ReLU: нелинейная функция активации. Это простая функция, возвращающая 0, если входные данные отрицательны, и входные данные, если они положительны. Это позволяет модели обучаться нелинейным функциям. Вычисления выглядят так:

262eac2557430f65416a724b1505a335.png

  1. Второй линейный слой: он противоположен первому линейному слою. Этот слой снова возвращает размерность к исходной. В нашем примере он выполнит снижение с 8 до 4.

Всё это можно описать следующим образом

bbc6f12f046194f7a985ee22eeb560c8.png

Напомню, что входными данными для этого слоя является Z, которое мы вычислили в самовнимании. Вот какие значения мы там получили

98bd6018fe81f8a9ce807877020cc5d8.png

Теперь давайте зададим произвольные значения для матриц весов и векторов смещений. Я сделаю это в коде, но если у вас хватит терпения, то можете задать их вручную!

W1 = np.random.randn(4, 8)
W2 = np.random.randn(8, 4)
b1 = np.random.randn(8)
b2 = np.random.randn(4)

А теперь давайте запишем функцию прямого прохода

def relu(x):
    return np.maximum(0, x)

def feed_forward(Z, W1, b1, W2, b2):
    return relu(Z.dot(W1) + b1).dot(W2) + b2
output_encoder = feed_forward(Z, W1, b1, W2, b2)
output_encoder
array([[ -3.24115016,  -9.7901049 , -29.42555675, -19.93135286],
       [ -3.40199463,  -9.87245924, -30.05715408, -20.05271018]])

5.2 Объединяем всё: произвольный кодировщик

Теперь давайте напишем код, чтобы объединить в блоке кодировщика многоголовое внимание и прямую связь.

Примечание

Код оптимизирован для понимания и образовательных целей, а не для производительности, не судите слишком строго!

d_embedding = 4
d_key = d_value = d_query = 3
d_feed_forward = 8
n_attention_heads = 2

def attention(x, WQ, WK, WV):
    K = x @ WK
    V = x @ WV
    Q = x @ WQ

    scores = Q @ K.T
    scores = scores / np.sqrt(d_key)
    scores = softmax(scores)
    scores = scores @ V
    return scores

def multi_head_attention(x, WQs, WKs, WVs):
    attentions = np.concatenate(
        [attention(x, WQ, WK, WV) for WQ, WK, WV in zip(WQs, WKs, WVs)], axis=1
    )
    W = np.random.randn(n_attention_heads * d_value, d_embedding)
    return attentions @ W

def feed_forward(Z, W1, b1, W2, b2):
    return relu(Z.dot(W1) + b1).dot(W2) + b2

def encoder_block(x, WQs, WKs, WVs, W1, b1, W2, b2):
    Z = multi_head_attention(x, WQs, WKs, WVs)
    Z = feed_forward(Z, W1, b1, W2, b2)
    return Z

def random_encoder_block(x):
    WQs = [
        np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)
    ]
    WKs = [
        np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)
    ]
    WVs = [
        np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)
    ]
    W1 = np.random.randn(d_embedding, d_feed_forward)
    b1 = np.random.randn(d_feed_forward)
    W2 = np.random.randn(d_feed_forward, d_embedding)
    b2 = np.random.randn(d_embedding)
    return encoder_block(x, WQs, WKs, WVs, W1, b1, W2, b2)

Вспомним наши входные данные в матрице E, имеющие позиционное кодирование и эмбеддинг.

embedding
array([[1.  , 3.  , 3.  , 5.  ],
       [2.84, 3.99, 4.  , 6.  ]])

Теперь передадим это нашей функции random_encoder_block

random_encoder_block(embedding)
array([[ -71.76537515, -131.43316885,   13.2938131 ,   -4.26831998],
       [ -72.04253781, -131.84091347,   13.3385937 ,   -4.32872015]])

Отлично! Это был всего один блок кодировщика. В научной статье применяются шесть кодировщиков. Выходные данные одного кодировщика передаются на следующий и так далее:

def encoder(x, n=6):
    for _ in range(n):
        x = random_encoder_block(x)
    return x


encoder(embedding)
/tmp/ipykernel_11906/1045810361.py:2: RuntimeWarning: overflow encountered in exp
  return np.exp(x)/np.sum(np.exp(x),axis=1, keepdims=True)
/tmp/ipykernel_11906/1045810361.py:2: RuntimeWarning: invalid value encountered in divide
  return np.exp(x)/np.sum(np.exp(x),axis=1, keepdims=True)
array([[nan, nan, nan, nan],
       [nan, nan, nan, nan]])

5.3 Остаточные связи и нормализация слоёв

Ой-ёй! У нас начали появляться NaN! Похоже, наши значения слишком велики и при передаче следующему кодировщику они оказываются слишком большими и «взрываются»! Эта проблема слишком больших значений часто возникает при обучении моделей. Например, когда мы выполняем обратное распространение ошибки (методику, при помощи которой модели обучаются), градиенты могут оказаться слишком большими и в результате «взрываются»; это называется взрывом градиентов (gradient explosion). Без нормализации небольшие изменения во входных данных на первых слоях в последующих слоях усиливаются. Это распространённая проблема в глубоких нейросетях. Существует два способа борьбы с этой проблемой: остаточные связи и нормализация слоёв (они вкратце упоминаются в разделе 3.1 научной статьи).

  • Остаточные связи просто прибавляют входные данные слоя к его выходным данным. Например, мы складываем исходный эмбеддинг с выходными данными внимания. Остаточные связи устраняют проблему исчезающих градиентов. Логика в том, что если градиент слишком мал, то мы можем просто сложить входные данные к выходным, и градиент станет больше. Вычисления очень просты:

f57ea26cb87a7dc176fe66b656dc2bbb.png

Вот и всё! Мы сделаем это для выходных данных внимания и выходных данных слоя с прямой связью.

  • Нормализация слоя — это методика нормализации входных данных слоя. Она выполняет нормализацию по размерности эмбеддинга. Логика в том, что мы хотим нормализовать входные значения слоя, чтобы они имели среднее значение 0 и квадратическое отклонение 1. Это помогает с градиентным потоком. Вычисления на первый взгляд выглядят не так уж просто.

e86b11dab9af842f994c4919c2e5d7ab.png

Давайте объясним каждый параметр:

  • μ — это среднее значение эмбеддинга

  • σ — это квадратическое отклонение эмбеддинга

  • ε — это малое число, чтобы избежать деления на ноль. В случае нулевого значения квадратичного отклонения этот маленький эпсилон спасает нас.

  • γ и β — это изучаемые параметры, управляющие этапами масштабирования и сдвига.

В отличие от пакетной нормализации (batch normalization, не волнуйтесь, если не знаете, что это такое), нормализация слоёв нормализует по размерности эмбеддинга; это означает, что на каждый эмбеддинг не будут влиять другие сэмплы в пакете. Идея заключается в том, что мы хотим нормализовать входные данные слоя, чтобы они имели среднее значение 0 и квадратичное отклонение 1.

Зачем мы добавляем изучаемые параметры γ и β? Причина в том, что мы не хотим терять силу представления слоя. Если просто нормализовать входные данные, то какая-то информация может потеряться. Добавляя изучаемые параметры, мы можем научиться масштабировать и сдвигать нормализованные значения.

Соединив эти уравнения, мы получим уравнение для всего кодировщика:

a0ac41a886c0c090a94831b723273008.png

Давайте проверим его на нашем примере! Возьмём прежние значения E и Z:

93bf47f27dedfcf295a42d2a389532c0.png

Теперь давайте вычислим нормализацию слоя; можно разделить этот процесс на три этапа:

  1. Вычисление среднего и дисперсии для каждого эмбеддинга.

  2. Нормализация вычитанием среднего в своей строке и делением на квадратный корень дисперсии строки (плюс малое число, чтобы избежать деления на ноль).

  3. Масштабирование и сдвиг умножением на гамму и прибавлением беты.

5.3.1 Среднее и дисперсия

Для первого эмбеддинга

7612e4d1500e7da378314073941be8ec.png

То же самое можно сделать для второго эмбеддинга. Пропустим сами вычисления и покажем только результат.

18f35a79565b79570fe341e8b6d85172.png

Давайте проверим при помощи Python

(embedding + Z).mean(axis=-1, keepdims=True)
array([[-4.58837567],
       [-3.59559107]])
(embedding + Z).std(axis=-1, keepdims=True)
array([[ 9.92061529],
       [10.50653019]])

Отлично! Теперь нормализуем

5.3.2 Нормализация

При нормализации из каждого значения в эмбеддинге мы вычитаем среднее и делим его на квадратичное отклонение. Эпсилон — это очень маленькое значение, например, 0,00001. Чтобы упростить, будем считать, что γ = 1, а β = 0.

ffe25dfe71f08897906a58c82bd44a0f.png

Для второго эмбеддинга мы не будем выполнять вычисления вручную. Проверим их при помощи кода. Переопределим функцию encoder_block, внеся следующее изменение:

def layer_norm(x, epsilon=1e-6):
    mean = x.mean(axis=-1, keepdims=True)
    std = x.std(axis=-1, keepdims=True)
    return (x - mean) / (std + epsilon)

def encoder_block(x, WQs, WKs, WVs, W1, b1, W2, b2):
    Z = multi_head_attention(x, WQs, WKs, WVs)
    Z = layer_norm(Z + x)

    output = feed_forward(Z, W1, b1, W2, b2)
    return layer_norm(output + Z)
layer_norm(Z + embedding)
array([[ 1.71887693, -0.56365339, -0.40370747, -0.75151608],
       [ 1.71909039, -0.56050453, -0.40695381, -0.75163205]])

Сработало! Давайте ещё раз попробуем пропустить эмбеддинг через шесть кодировщиков.

def encoder(x, n=6):
    for _ in range(n):
        x = random_encoder_block(x)
    return x


encoder(embedding)
array([[-0.335849  , -1.44504571,  1.21698183,  0.56391289],
       [-0.33583947, -1.44504861,  1.21698606,  0.56390202]])

Отлично! Значения приемлемые и отсутствуют NaN! Идея стека кодировщиков заключается в том, что на выходе они выдают непрерывное описание z, передающее смысл входной последовательности. Затем это описание передаётся декодеру, который генерирует выходную последовательность символов по одному элементу за раз.

Прежде чем приступать к декодеру, взглянем на изображение из потрясающего поста Джея:

Кодировщик и декодер
Кодировщик и декодер

Каждый из элементов в левой части должен быть вам уже понятен! Впечатляет, правда? А теперь давайте перейдём к декодеру.

Декодер

Большинство знаний, полученных при изучении кодировщиков, будет использоваться и в декодере! Декодер имеет два слоя самовнимания, один для кодировщика, другой для декодера. Также декодер имеет слой с прямой связью. Давайте разберём каждую из частей по порядку.

Блок декодера получает два элемента входных данных: выходные данные кодировщика и сгенерированную выходную последовательность. Выходные данные кодировщика — это описание входной последовательности. В процессе инференса сгенерированная выходная последовательность начинается с особого токена начала последовательности (start-of-sequence token, SOS). Во время обучения целевая выходная последовательность — это действительная выходная последовательность, сдвинутая на одну позицию. Скоро это станет вам понятнее!

Имея сгенерированный кодировщиком эмбеддинг и токен SOS, декодер генерирует следующий токен последовательности, то есть «hola». Декодер авторегрессивен, то есть он берёт ранее сгенерированные токены и снова генерирует второй токен.

  • Итерация 1: входные данные — SOS, выходные — «hola»

  • Итерация 2: входные данные — SOS + «hola», выходные — «mundo»

  • Итерация 3: входные данные — SOS + «hola» + «mundo», выходные — EOS

Здесь SOS — это токен начала последовательности, а EOS — токен конца последовательности. После генерации токена EOS декодер прекращает работу. Он генерирует по одному токену за раз. Обратите внимание, что во всех итерациях используется эмбеддинг, сгенерированный кодировщиком.

Примечание

Такая авторегрессивная структура замедляет работу декодера. Кодировщик способен генерировать свой эмбеддинг за один прямой проход, а декодеру необходимо выполнить множество прямых проходов. Это одна из причин, по которым архитектуры, использующие один кодировщик (например, BERT или модели схожести предложений) гораздо быстрее, чем архитектуры с одними только декодерами (например, GPT-2 или BART).

Давайте разберём каждый из этапов! Как и кодировщик, декодер состоит из стека блоков декодеров. Блок декодера чуть сложнее, чем блок кодировщика. Его общая структура такова:

  1. Слой самовнимания (маскированный)

  2. Остаточная связь и нормализация слоя

  3. Слой внимания кодировщика-декодера

  4. Остаточная связь и нормализация слоя

  5. Слой с прямой связью

  6. Остаточная связь и нормализация слоя

Мы уже знакомы со всей математикой пунктов 1, 2, 3, 5 и 6. Взглянув на правую часть изображения ниже, вы увидите, что все эти блоки вам уже известны :

Модель трансформера из статьи «Attention is all you need»
Модель трансформера из статьи «Attention is all you need»

1. Эмбеддинг текста

Первый текст декодера нужен для эмбеддинга входных токенов. Входным токеном является SOS, так что мы выполняем его эмбеддинг. Используется та же размерность эмбеддинга, что и для кодировщика. Предположим, вектор эмбеддинга для SOS имеет такой вид:

35f571ab480469598afaf2272b2ac2ea.png

2. Позиционное кодирование

Теперь мы добавим в эмбеддинг позиционное кодирование, как делали это в случае с кодировщиком. Учитывая, что это так же позиция, что и у «Hello», у нас будет то же позиционное кодирование, что и раньше:

  • i = 0 (чётный): PE(0,0) = sin(0 / 10000^(0 / 4)) = sin(0) = 0

  • i = 1 (нечётный): PE(0,1) = cos(0 / 10000^(2*1 / 4)) = cos(0) = 1

  • i = 2 (чётный): PE(0,2) = sin(0 / 10000^(2*2 / 4)) = sin(0) = 0

  • i = 3 (нечётный): PE(0,3) = cos(0 / 10000^(2*3 / 4)) = cos(0) = 1

3. Сложение позиционного кодирования и эмбеддинга

Сложение позиционного кодирования с эмбеддингом выполняется сложением двух векторов:

94c8d59a4656853cd52979ac450b716b.png

4. Самовнимание

Первый этап в блоке декодера — это механизм самовнимания. К счастью, у нас есть для этого код и мы можем просто его использовать!

d_embedding = 4
n_attention_heads = 2

E = np.array([[1, 1, 0, 1]])
WQs = [np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)]
WKs = [np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)]
WVs = [np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)]

Z_self_attention = multi_head_attention(E, WQs, WKs, WVs)
Z_self_attention
array([[ 2.19334924, 10.61851198, -4.50089666, -2.76366551]])

Примечание

С точки зрения инференса всё довольно просто, однако с точки зрения обучения есть сложности. При обучении мы используем неразмеченные данные: просто кучу текстовых данных, которые собираем частым скрейпингом в вебе. Цель кодировщика — передача всей информации входных данных, а задача декодера —предсказание следующего наиболее вероятного токена. Это значит, что декодер может использовать только ранее сгенерированные токены (он не может схитрить и посмотреть следующие токены).

Из-за этого мы используем маскированное самовнимание: маскируем ещё не сгенерированные токены. Это выполняется присвоением показателям внимания значений -inf. Так делается в научной статье (раздел 3.2.3.1). Пока мы это пропустим, но важно помнить, что при обучении декодер чуть сложнее.

5. Остаточные связи и нормализация слоёв

Здесь нет ничего таинственного, мы просто складываем входные данные с выходными данными самовнимания и применяем нормализацию слоя. Используется тот же код, что и выше.

Z_self_attention = layer_norm(Z_self_attention + E)
Z_self_attention
array([[ 0.17236212,  1.54684892, -1.0828824 , -0.63632864]])

6. Внимание кодировщика-декодера

Эта часть новая! Если вы задавались вопросом, куда направляются генерируемые кодировщиком эмбеддинги, то сейчас самое время для них!

Предположим, что выходными данными кодировщика является такая матрица:

fc2024fb11fec40a9e7153c6615fc0ce.png

В механизме самовнимания мы вычисляем запросы, ключи и значения для входного эмбеддинга.

Во внимании кодировщика-декодера мы вычисляем запросы из предыдущего слоя декодера и ключи и значения из выходных данных кодировщика! Все вычисления остаются такими же, что и раньше; единственное отличие в том, какой эмбеддинг использовать для запросов. Давайте взглянем на код

def encoder_decoder_attention(encoder_output, attention_input, WQ, WK, WV):
    # В следующих трёх строках и состоит основное различие!
    K = encoder_output @ WK    # Обратите внимание, что теперь мы передаём предыдущие выходные данные кодировщика!
    V = encoder_output @ WV    # Обратите внимание, что теперь мы передаём предыдущие выходные данные кодировщика!
    Q = attention_input @ WQ   # То же, что и для самовнимания

    # Остаётся таким же
    scores = Q @ K.T
    scores = scores / np.sqrt(d_key)
    scores = softmax(scores)
    scores = scores @ V
    return scores


def multi_head_encoder_decoder_attention(
    encoder_output, attention_input, WQs, WKs, WVs
):
    # Обратите внимание, что теперь мы передаём предыдущие выходные данные кодировщика!
    attentions = np.concatenate(
        [
            encoder_decoder_attention(
                encoder_output, attention_input, WQ, WK, WV
            )
            for WQ, WK, WV in zip(WQs, WKs, WVs)
        ],
        axis=1,
    )
    W = np.random.randn(n_attention_heads * d_value, d_embedding)
    return attentions @ W
WQs = [np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)]
WKs = [np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)]
WVs = [np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)]

encoder_output = np.array([[-1.5, 1.0, -0.8, 1.5], [1.0, -1.0, -0.5, 1.0]])

Z_encoder_decoder = multi_head_encoder_decoder_attention(
    encoder_output, Z_self_attention, WQs, WKs, WVs
)
Z_encoder_decoder
array([[ 1.57651431,  4.92489307, -0.08644448, -0.46776051]])

Сработало! Возможно, вы зададитесь вопросом: «зачем мы это делаем?». Дело в том, что мы хотим, чтобы декодер сосредоточился на релевантных частях входного текста (то есть «hello world»). Внимание кодировщика-декодера позволяет каждой позиции в декодере посетить все позиции входной последовательности. Это очень полезно для таких задач, как перевод, когда декодеру нужно сосредоточиться на релевантных частях входной последовательности. Декодер будет учиться сосредотачиваться на релевантных частях входной последовательности, учась генерировать правильные выходные токены. Это очень мощный механизм!

7. Остаточные связи и нормализация слоя

Всё то же, что и раньше!

Z_encoder_decoder = layer_norm(Z_encoder_decoder + Z_self_attention)
Z_encoder_decoder
array([[-0.44406723,  1.6552893 , -0.19984632, -1.01137575]])

8. Слой с прямой связью

И тут то же самое! После этого я также выполню остаточную связь и нормализацию слоя.

W1 = np.random.randn(4, 8)
W2 = np.random.randn(8, 4)
b1 = np.random.randn(8)
b2 = np.random.randn(4)

output = layer_norm(feed_forward(Z_encoder_decoder, W1, b1, W2, b2) + Z_encoder_decoder)
output
array([[-0.97650182,  0.81470137, -2.79122044, -3.39192873]])

9. Объединяем всё: произвольный декодер

Давайте напишем код для одного блока декодера. Самое главное изменение заключается в том, что теперь у нас есть дополнительный механизм внимания.

d_embedding = 4
d_key = d_value = d_query = 3
d_feed_forward = 8
n_attention_heads = 2
encoder_output = np.array([[-1.5, 1.0, -0.8, 1.5], [1.0, -1.0, -0.5, 1.0]])

def decoder_block(
    x,
    encoder_output,
    WQs_self_attention, WKs_self_attention, WVs_self_attention,
    WQs_ed_attention, WKs_ed_attention, WVs_ed_attention,
    W1, b1, W2, b2,
):
    # То же, что и раньше
    Z = multi_head_attention(
        x, WQs_self_attention, WKs_self_attention, WVs_self_attention
    )
    Z = layer_norm(Z + x)

    # Основное различие заключается в следующих трёх строках!
    Z_encoder_decoder = multi_head_encoder_decoder_attention(
        encoder_output, Z, WQs_ed_attention, WKs_ed_attention, WVs_ed_attention
    )
    Z_encoder_decoder = layer_norm(Z_encoder_decoder + Z)

    # То же, что и раньше
    output = feed_forward(Z_encoder_decoder, W1, b1, W2, b2)
    return layer_norm(output + Z_encoder_decoder)

def random_decoder_block(x, encoder_output):
    # Просто несколько произвольных инициализаций
    WQs_self_attention = [
        np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)
    ]
    WKs_self_attention = [
        np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)
    ]
    WVs_self_attention = [
        np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)
    ]

    WQs_ed_attention = [
        np.random.randn(d_embedding, d_query) for _ in range(n_attention_heads)
    ]
    WKs_ed_attention = [
        np.random.randn(d_embedding, d_key) for _ in range(n_attention_heads)
    ]
    WVs_ed_attention = [
        np.random.randn(d_embedding, d_value) for _ in range(n_attention_heads)
    ]

    W1 = np.random.randn(d_embedding, d_feed_forward)
    b1 = np.random.randn(d_feed_forward)
    W2 = np.random.randn(d_feed_forward, d_embedding)
    b2 = np.random.randn(d_embedding)


    return decoder_block(
        x, encoder_output,
        WQs_self_attention, WKs_self_attention, WVs_self_attention,
        WQs_ed_attention, WKs_ed_attention, WVs_ed_attention,
        W1, b1, W2, b2,
    )
def decoder(x, decoder_embedding, n=6):
    for _ in range(n):
        x = random_decoder_block(x, decoder_embedding)
    return x

decoder(E, encoder_output)
array([[ 0.25919176,  1.49913566, -1.14331487, -0.61501256],
       [ 0.25956188,  1.49896896, -1.14336934, -0.61516151]])

Генерация выходной последовательности

У нас уже есть все необходимые части! Давайте сгенерируем выходную последовательность.

  • У нас есть кодировщик, получающий входную последовательность и генерирующий его обогащённое описание. Он состоит из стека блоков кодировщиков.

  • У нас есть декодер, получающий выходные данные кодировщика и сгенерированные токены и генерирующий выходную последовательность. Он состоит из стека блоков декодеров.

Как перейти от выходных данных декодера к слову? Нужно добавить поверх декодера последний линейный слой и слой softmax. Весь алгоритм в целом выглядит так:

  1. Обработка кодировщиком: кодировщик получает входную последовательность и генерирует контекстуализированное описание всего предложения при помощи стека блоков кодировщиков.

  2. Инициализация декодера: процесс декодирования начинается с эмбеддинга токена SOS (Start of Sequence), соединённого с выходными данными кодировщика.

  3. Работа декодера: декодер использует выходные данные кодировщика и эмбеддинги всех ранее сгенерированных токенов для создания нового списка эмбеддингов.

  4. Линейный слой для логитов: линейный слой применяется к последнему выходному эмбеддингу декодера для генерации логитов, представляющих сырые предсказания следующего токена.

  5. Softmax для вероятностей: затем эти логиты передаются через слой softmax, преобразующий их в распределение вероятностей по потенциальным следующим токенам.

  6. Итеративная генерация токенов: этот процесс повторяется, и на каждом этапе декодер генерирует следующий токен на основании кумулятивных эмбеддингов ранее сгенерированных токенов и исходных выходных данных кодировщика.

  7. Формирование предложения: эти этапы генерации продолжаются, пока не будет создан токен EOS (End of Sequence) или не достигнута заранее заданная максимальная длина предложения.

Об этом говорится в разделе 3.4 научной статьи.

1. Линейный слой

Линейный слой — это простое линейное преобразование. Он получает выходные данные декодера и преобразует их в вектор размера vocab_size. Это размер словаря. Например, если у нас есть словарь из 10000 слов, то линейный слой преобразовал бы выходные данные декодера в вектор размера 10000. Этот вектор содержал бы вероятность того, что каждое слово будет следующим словом в последовательности. Для простоты можно начать со словаря из 10 слов и предположить, что первые выходные данные декодера — это очень простой вектор: [1, 0, 1, 0]. Мы используем произвольные веса и матрицы перекосов размера vocab_size x decoder_output_size.

def linear(x, W, b):
    return np.dot(x, W) + b

x = linear([1, 0, 1, 0], np.random.randn(4, 10), np.random.randn(10))
x
array([ 0.06900542, -1.81351091, -1.3122958 , -0.33197364,  2.54767851,
       -1.55188231,  0.82907169,  0.85910931, -0.32982856, -1.26792439])

Примечание

Что используется в качестве входных данных для линейного слоя? Декодер будет выводить по одному эмбеддингу для каждого токена в последовательности. Входными данными для линейного слоя станет последний сгенерированный эмбеддинг. Последний эмбеддинг включает в себя информацию для всей последовательности до этого этапа, то есть содержит всю информацию, необходимую для генерации следующего токена. Это значит, что каждый выходной эмбеддинг декодера содержит информацию о всей последовательности до этого этапа.

2. Softmax

Они называются логитами, но интерпретировать их не так просто. Для получения вероятностей можно применить функцию softmax.

softmax(x)
array([[0.01602618, 0.06261303, 0.38162024, 0.03087794, 0.0102383 ,
        0.00446011, 0.01777314, 0.00068275, 0.46780959, 0.00789871]])

И так мы получили вероятности! Предположим, словарь имеет такой вид:

af1ce2cd67a1bfc1e3def62b9b09cc96.png

Мы видим, что вероятности таковы:

  • hello: 0.01602618

  • mundo: 0.06261303

  • world: 0.38162024

  • how: 0.03087794

  • ?: 0.0102383

  • EOS: 0.00446011

  • SOS: 0.01777314

  • a: 0.00068275

  • hola: 0.46780959

  • c: 0.00789871

Из этого видно, что наиболее вероятный следующий токен — это «hola». Если всегда выбирается наиболее вероятный токен, это называется жадным декодингом. Это не всегда наилучший подход, потому что он может привести к субоптимальным результатам, но пока мы не будем сейчас углубляться в методики генерации. Если хотите узнать о них подробнее, то прочитайте потрясающий пост.

3. Случайный трансформер из кодировщика и декодера

Давайте напишем код целиком. Зададим словарь, сопоставляющий слова с их изначальными эмбеддингами. Надо отменить, что это тоже изучается при обучении, но пока мы используем случайные значения.

vocabulary = [
    "hello",
    "mundo",
    "world",
    "how",
    "?",
    "EOS",
    "SOS",
    "a",
    "hola",
    "c",
]
embedding_reps = np.random.randn(10, 4)
vocabulary_embeddings = {
    word: embedding_reps[i] for i, word in enumerate(vocabulary)
}
vocabulary_embeddings
{'hello': array([-0.32106406,  2.09332588, -0.77994069,  0.92639774]),
 'mundo': array([-0.59563791, -0.63389256,  1.70663692, -0.99495115]),
 'world': array([ 1.35581862, -0.0323546 ,  2.76696887,  0.83069982]),
 'how': array([-0.52975474,  0.94439644,  0.80073818, -1.50135518]),
 '?': array([-0.88116833,  0.13995055,  2.01827674, -0.52554391]),
 'EOS': array([1.12207024, 1.40905796, 1.22231714, 0.02267638]),
 'SOS': array([-0.60624082, -0.67560165,  0.77152125,  0.63472247]),
 'a': array([ 1.67622229, -0.20319309, -0.18324905, -0.24258774]),
 'hola': array([ 1.07809402, -0.83846408, -0.33448976,  0.28995976]),
 'c': array([ 0.65643157,  0.24935726, -0.80839751, -1.87156293])}

А теперь напишем произвольный метод generate , авторегрессивно генерирующий токены.

def generate(input_sequence, max_iters=3):
    # Сначала мы кодируем входные данные в эмбеддинги
    # Для простоты мы пропустим этап позиционного кодирования
    embedded_inputs = [
        vocabulary_embeddings[token] for token in input_sequence
    ]
    print("Embedding representation (encoder input)", embedded_inputs)

    # Затем генерируем описание эмбеддинга
    encoder_output = encoder(embedded_inputs)
    print("Embedding generated by encoder (encoder output)", encoder_output)

    # Инициализируем выходные данные декодера эмбеддингом начального токена
    sequence_embeddings = [vocabulary_embeddings["SOS"]]
    output = "SOS"
    
    # Случайные матрицы для линейного слоя
    W_linear = np.random.randn(d_embedding, len(vocabulary))
    b_linear = np.random.randn(len(vocabulary))

    # Мы ограничиваем количество этапов декодинга, чтобы избежать слишком последовательностей без EOS
    for i in range(max_iters):
        # Этап декодера
        decoder_output = decoder(sequence_embeddings, encoder_output)

        # Используем для предсказания только последние выходные данные
        logits = linear(decoder_output[-1], W_linear, b_linear)
        # Обёртываем логиты в список, потому что softmax нужны пакеты/2D-массив
        probs = softmax([logits])

        # Получаем наиболее вероятный следующий токен
        next_token = vocabulary[np.argmax(probs)]
        sequence_embeddings.append(vocabulary_embeddings[next_token])
        output += " " + next_token

        print(
            "Iteration", i, 
            "next token", next_token,
            "with probability of", np.max(probs),
        )

        # Если следующий токен последний, то возвращаем последовательность
        if next_token == "EOS":
            return output

    return output, sequence_embeddings

Давайте запустим код!

generate(["hello", "world"])
Embedding representation (encoder input) [array([-0.32106406,  2.09332588, -0.77994069,  0.92639774]), array([ 1.35581862, -0.0323546 ,  2.76696887,  0.83069982])]
Embedding generated by encoder (encoder output) [[ 1.14747807 -1.5941759   0.36847675  0.07822107]
 [ 1.14747705 -1.59417696  0.36847441  0.07822551]]
Iteration 0 next token hola with probability of 0.4327111653266739
Iteration 1 next token mundo with probability of 0.4411354383451089
Iteration 2 next token world with probability of 0.4746898792307499
('SOS hola mundo world',
 [array([-0.60624082, -0.67560165,  0.77152125,  0.63472247]),
  array([ 1.07809402, -0.83846408, -0.33448976,  0.28995976]),
  array([-0.59563791, -0.63389256,  1.70663692, -0.99495115]),
  array([ 1.35581862, -0.0323546 ,  2.76696887,  0.83069982])])

Отлично, теперь у нас есть токены «how», «a» и «c». Это неправильный перевод, но этого вполне можно было ожидать, ведь веса мы использовали случайные.

Советую ещё раз подробно изучить всю архитектуру кодировщика-декодера из научной статьи:

Кодировщик и декодер
Кодировщик и декодер

Заключение

Надеюсь, пост показался вам интересным и информативным! Мы рассмотрели множество аспектов. Но разве это всё? На самом деле, практически да! В архитектуры новых трансформеров добавляют множество трюков, но фундамент трансформера именно таков, каким мы его описали. В зависимости от задачи также можно использовать только кодировщик или декодер. Например, в задачах, требующих понимания, например, в классификации, можно использовать стек кодировщиков с линейным слоем поверх него. Для задач, требующих генерации, например, в переводе, можно использовать стеки кодировщиков и декодеров. А для свободной генерации, например, как в ChatGPT или Mistral, можно применять только стек декодеров.

Разумеется, мы многое упростили. Давайте вкратце проверим, какие были числа в научной статье о трансформере:

  • Размерность эмбеддингов: 512 (в нашем примере 4)

  • Количество кодировщиков: 6 (в нашем примере 6)

  • Количество декодеров: 6 (в нашем примере 6)

  • Размерность прямой связи: 2048 (в нашем примере 8)

  • Количество голов внимания: 8 (в нашем примере 2)

  • Размерность внимания: 64 (в нашем примере 3)

Мы рассмотрели множество тем, но довольно интересно, то мы можем достичь впечатляющих результатов, увеличив масштабы этих вычислений и проведя умное обучение. Мы не рассмотрели в посте обучение, потому что наша цель заключалась в понимании вычислений при использовании готовой модели, но я надеюсь, что это станет надёжным фундаментом для перехода к обучению!

Также можно найти более формальный документ с вычислениями в этом PDF.

Упражнения

Вот несколько упражнений, чтобы попрактиковаться в понимании трансформера.

  1. В чём предназначение позиционного кодирования?

  2. Чем отличаются самовнимание и внимание кодировщика-декодера?

  3. Что произойдёт, если размерность внимания слишком мала? А если слишком велика?

  4. Вкратце опишите структуру слоя с прямой связью.

  5. Почему декодер медленнее кодировщика?

  6. Какова цель остаточных связей и нормализации слоёв?

  7. Как выполняется переход от выходных данных декодера к вероятностям?

  8. Почему выбор каждый раз самого вероятного следующего токена может вызвать проблемы?

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  • 08.09.25 18:04 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 08.09.25 18:04 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 08.09.25 19:21 DAVEortega1010

    Be wary of fraudulent cryptocurrency recovery services. Many promise to recover your lost digital currency. These services often provide excuses or fail to deliver any results. This only adds to your distress. After several unsuccessful attempts with others, I discovered a genuine expert. This individual was highly capable and provided excellent assistance. They successfully recovered my stolen cryptocurrency. I was finally able to find peace of mind. If you have lost crypto, you should contact them. talk to [email protected] for help. You can also send a text message via WhatsApp to +447366445035, Stop losing time on scams. They can help you get your money back.

  • 09.09.25 02:34 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.09.25 02:34 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.09.25 02:34 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.09.25 11:48 Moises Velez

    I strongly advise using this very reputable Recovery Hacker101for anyone looking to recover any type of crypto currencies assets from online frauds, Wallet hackers, or BTC transferred to the wrong address. After I lost a lot of money to those terrible con artists posing as recovery specialists, this recovery specialist was great in aiding me in getting my Bitcoin back. After I gave Recovery Hacker101 the relevant details and prerequisites, a total of 1.4170 BTC was eventually recovered. I was overjoyed that I had been able to recover this much after having lost even more to the problems I had dealt with before discovering Recovery Hacker101. So don’t hesitate to get in touch with recoveryhacker101 AT gmail com. if you find yourself in this scenario and need help recovering from an online bitcoin scam

  • 09.09.25 15:05 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.09.25 15:05 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.09.25 15:05 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 09.09.25 20:23 Bramfloris

    Recovering Stolen USDT If your USDT or other crypto assets were stolen, contact Sylvester Bryant at Yt7cracker@gmail. com. He can help you get your money back. I lost €220,000 in a scam. Mr. Bryant was the only expert who successfully recovered my funds. Reach him on WhatsApp at +1 512 577 7957 for fast, expert help. He is very honest. He can recover your stolen assets.

  • 09.09.25 20:37 DAVEortega1010

    Be wary of fraudulent cryptocurrency recovery services. Many promise to recover your lost digital currency. These services often provide excuses or fail to deliver any results. This only adds to your distress. After several unsuccessful attempts with others, I discovered a genuine expert. This individual was highly capable and provided excellent assistance. They successfully recovered my stolen cryptocurrency. I was finally able to find peace of mind. If you have lost crypto, you should contact them. talk to [email protected] for help. You can also send a text message via WhatsApp to +447366445035, Stop losing time on scams. They can help you get your money back.

  • 10.09.25 00:45 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 10.09.25 00:45 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.09.25 03:31 DAVEortega1010

    Be wary of fraudulent cryptocurrency recovery services. Many promise to recover your lost digital currency. These services often provide excuses or fail to deliver any results. This only adds to your distress. After several unsuccessful attempts with others, I discovered a genuine expert. This individual was highly capable and provided excellent assistance. They successfully recovered my stolen cryptocurrency. I was finally able to find peace of mind. If you have lost crypto, you should contact them. talk to [email protected] for help. You can also send a text message via WhatsApp to +447366445035, Stop losing time on scams. They can help you get your money back.

  • 11.09.25 13:44 grace

    i fell for an investment scam also and lost $250k worth of bitcoin luckily i found anthonydavies01 on telegram with his assistance i got back over 85% of my money. him and his team are top notch

  • 11.09.25 15:03 stevensjonas

    Recovery of Stolen Ethereum Wallet. Hire: Supreme Peregrine Recovery. I would like to express my sincere gratitude to Supreme Peregrine Recovery for their outstanding help in recovering my stolen Ethereum wallet, which held $594,684 worth of assets. I thought my money was lost forever after falling for a scam that imitated a reliable cryptocurrency platform, but I was referred to them because their staff was professional, knowledgeable, and genuinely concerned from the start. Their commitment, openness, and expertise are unparalleled. I am immensely appreciative of their assistance and heartily recommend Supreme Peregrine Recovery to anyone dealing with cryptocurrency theft. They transformed a nightmare into a tale of hope and recovery. They carefully examined my case, gave me clear updates at every stage, and used cutting-edge Blockchain tracing tools to recover the entire amount. +1,3,1,8,5,5,3,0,6,7,9 Mail: supremeperegrinerecovery(@)proton(.)me supremeperegrinerecovery567(@)zohomail(.)com info(@)supremeperegrinerecovery(.)com

  • 11.09.25 18:51 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.09.25 18:51 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.09.25 18:51 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. Contact: [email protected]  You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 12.09.25 13:11 grace

    I lost my money to them few months ago. I lost over $244,000, they denied my withdrawal request and and also left it pending. I reached out to them and they never responded back tooth my emails and calls. They eventually locked me out of my account. I had to reach out to a recovery expert ( anthonydaviestech@gmail com) to help me recover all my money back. I have gotten my money back**you can also text him via whatsapp: +19514908435

  • 12.09.25 15:06 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 12.09.25 15:06 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 13.09.25 20:45 Clinton

    I know firsthand how devastating it feels to lose money to a scam. When it happened to me, I was left frustrated, hopeless, and unsure where to turn. Complaining to apps about being scammed on their platforms didn’t change anything it felt like no one cared. But through a friend’s advice, I connected with a recovery professional who gave me real hope. With their help, I was able to get my funds back, something I thought was impossible. I’m sharing this because I don’t want anyone else to feel as lost as I once did. Whether you’ve been scammed through crypto platforms, dating scams, real-estate or mortgage fraud, or even fake ICOs, please know there’s still a way forward. If you’ve lost money, reach out to Recoveryfundprovider(@)gmail(.)com).) or (WhatsApp) at (+)44 7366445035 for consultation and recovery services.

  • 14.09.25 00:54 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.09.25 00:54 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.09.25 02:37 luciajessy3

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  • 14.09.25 12:44 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.09.25 12:44 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.09.25 15:13 estherfords

    My solana recovery experience with Mighty Hacker Recovery Expert.

  • 14.09.25 15:13 estherfords

    My solana recovery experience with Mighty Hacker Recovery Expert. Contact them on +14042456415 WhatsApp

  • 14.09.25 17:48 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.09.25 17:48 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.09.25 20:49 Clinton

    I know firsthand how devastating it feels to lose money to a scam. When it happened to me, I was left frustrated, hopeless, and unsure where to turn. Complaining to apps about being scammed on their platforms didn’t change anything it felt like no one cared. But through a friend’s advice, I connected with a recovery professional who gave me real hope. With their help, I was able to get my funds back, something I thought was impossible. I’m sharing this because I don’t want anyone else to feel as lost as I once did. Whether you’ve been scammed through crypto platforms, dating scams, real-estate or mortgage fraud, or even fake ICOs, please know there’s still a way forward. If you’ve lost money, reach out to ([email protected]) or (WhatsApp) at (+)44 7366445035 for consultation and recovery services.

  • 14.09.25 22:16 Berrysmith

    I recently recovered a large sum of digital assets. Sylvester Bryant, reachable at Yt7cracker@gmail. com, helped me reclaim 720,000 in Ethereum. The entire experience was excellent. I highly recommend Mr. Sylvester. He assists those dealing with lost or stolen funds. His skill in getting back money from scams is outstanding. Scammers cause huge stress and financial pain. Mr. Bryant offers a crucial service. He provides a way to possibly recover stolen funds. His professional manner built trust. If you lost money to scams, contact him. He is also on WhatsApp at +1 512 577 7957. This makes it easy to discuss your case. Recovering this amount was difficult. Mr. Bryant showed deep knowledge of the technical work. His commitment to solving these problems is clear. Seek his help for lost crypto or other digital assets. This is a major concern for many. Expert aid can greatly improve outcomes.

  • 15.09.25 10:25 aliceforemanlaw

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  • 15.09.25 12:49 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.09.25 12:49 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.09.25 12:49 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 16.09.25 12:25 aliceforemanlaw

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  • 16.09.25 12:26 aliceforemanlaw

    Sylvester Bryant helped me recover 120,000 in Ethereum. You can reach him at Yt7cracker@gmail. com. It was a great experience overall. I really suggest Mr. Sylvester. He helps people who lost money. He is great at getting money back from scams. Scammers cause a lot of stress and hurt. Mr. Bryant offers an important service. He can help you get back stolen funds. He was very professional and earned my trust. Contact him if you lost money to scams. He is also on WhatsApp at +1 512 577 7957. This makes it easy to talk about your situation. Getting this amount back was tough. Mr. Bryant knew a lot about the technical parts. His drive to fix these issues is clear. Get his help if you lost crypto or other digital items. Many people worry about this. Getting expert help can really make a difference.

  • 16.09.25 13:25 marcushenderson624

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  • 16.09.25 13:25 marcushenderson624

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  • 17.09.25 02:56 peju1213

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  • 17.09.25 11:16 [email protected]

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  • 17.09.25 23:50 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 17.09.25 23:50 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 17.09.25 23:50 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 18.09.25 11:55 Mundo

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  • 18.09.25 11:55 Mundo

    Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.

  • 18.09.25 12:22 wendytaylor015

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  • 18.09.25 12:22 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 18.09.25 13:04 Mundo

    Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.

  • 18.09.25 16:46 carolinehudso83

    I noticed a lot of online recommendations, and it’s clear that some of them are bad eggs that will just make уour mуsterу worse. I can onlу suggest one, and if уou need assistance getting back the moneу уou lost to scammers, уou can contact them bу email at: [email protected] Whats app or text +1 518 468 2985 Website https://bestrecoveryagent.com/

  • 19.09.25 00:54 frank2025

    Anthony davies played a crucial role in successfully recovering my stolen USDT, which was valued at more than $300,000. His expertise and dedication made the recovery process smooth and efficient. Throughout the entire time, he demonstrated himself to be a reliable recovery agent. His professionalism and commitment to his clients are evident in the results he achieves. If you find yourself in a similar situation or need assistance, he is available for contact. You can reach anthony through email at (anthonydaviestech AT gmail dot com). Alternatively, he is also accessible via telegram at anthonydavies01. Reaching out to him could be the first step toward recovering your lost assets

  • 19.09.25 10:02 faithlawrence

    Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.

  • 19.09.25 10:02 faithlawrence

    Sylvester Bryant recovered £400,000 in Ethereum for me. I strongly advise using his services. He focuses on retrieving money lost to fraudulent schemes. Scams cause immense worry. Mr. Bryant's expert knowledge and calm approach in getting funds back reassured me. If you have lost money to scams, contact him via email at [email protected]. You can also reach him on WhatsApp at +1 512 577 7957. He is committed to helping people recover their stolen assets. His support was invaluable in my situation.

  • 19.09.25 15:27 tonykith01477

    There are not many reviews about free crypto recovery fixed but the ones that exist are mostly positive. I have no idea how that is possible, but it is clear that they are fabricated. However, there are also negative reviews – and I highly recommend paying attention to them. These are real people describing their unfortunate experiences with this scam. It’s the same story as always – fraudsters create a fake website to con people out of money. Nothing new but look no more and contact FASTRECOVERYAGENT These types of scams are everywhere. If you have already lost money to scammers i mean any type be it sending to scammers account , or if you have a case about stolen bitcoin , usdt, or any type of cryptocurrency whatsoever just reach out to www.fastrecoveryagent.com, i really owe this group of recovery expert because they saved me after bad investment with a fake broker, i literally owe them my life as they saved me from some bunch of scammers, but see how life is , i got every cent of my investment back with the profit , reach out to to them today and tell them from Mary because i promise them i will tell the whole world when the recovery is complete, and here i go after i got my recovered assets thats why im doing what i promised. do not fall for another scam. contact the,m today!!!!

  • 19.09.25 17:12 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 19.09.25 17:12 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 20.09.25 15:05 faithlawrence

    I can’t recommend Sylvester Bryant enough. He successfully recovered €210,000 in Ethereum for me after I had lost hope. His expertise in tracing and reclaiming funds from scams is truly remarkable. What stood out most was his calm, professional approach and deep technical knowledge, which gave me complete confidence throughout the process. If you’ve lost money to a scam, I strongly encourage you to reach out to him. You can contact him via email at [[email protected] ] or on WhatsApp at +1 512 577 7957. He is genuinely dedicated to helping people recover what they’ve lost, and his support has been invaluable to me.

  • 20.09.25 15:53 blessing1198

    It is distressing to lose USDT due to a bitcoin wallet hack. Although it is challenging, stolen USDT can be recovered. Taking prompt, wise action increases your chances. Marie can help you with reporting the theft, what to do right away, and USDT recovery. Contact her on WhatsApp at +1 7127594675, or email [email protected].

  • 21.09.25 12:05 star1121

    Consider this: In cryptocurrency, you see what appears to be a fantastic opportunity. After investing your hard-earned money, you see it disappear into the wallet of a con artist. Your bank account seems empty as rage and regret merge in this stomach punch. These days, cryptocurrency frauds are very common, however recovering your cryptocurrency from scammers is still possible. You can track down and possibly recover what you lost with shrewd actions. Marie can help; contact her at [email protected] and on WhatsApp at +1 7127594675.

  • 23.09.25 03:23 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.09.25 03:23 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.09.25 03:23 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.09.25 03:54 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 23.09.25 14:45 Raymondkrisitina

    Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.

  • 23.09.25 19:27 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider [email protected] WhatsApp at +44 736-644-5035 through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and I’m endlessly grateful.

  • 23.09.25 22:38 Raymondkrisitina

    Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.

  • 24.09.25 12:22 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider [email protected] WhatsApp at +44 736-644-5035 through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and I’m endlessly grateful.

  • 24.09.25 15:50 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.09.25 15:50 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.09.25 15:50 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance contact [email protected] and on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.09.25 19:08 Raymondkrisitina

    Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.

  • 24.09.25 19:50 Raymondkrisitina

    Sylvester Bryant gets my full recommendation. He helped me get back €230,000 in Ethereum when I thought it was gone forever. His skills in tracking and retrieving scam-lost funds amaze me. I appreciated his steady, expert manner and strong tech know-how. That built my trust every step of the way. If a scam has taken your money, get in touch with him right away. Email him at yt7cracker@gmail. com or message on WhatsApp at +1 512 577 7957. He truly commits to aiding folks in regaining their assets. His help meant everything to me.

  • 24.09.25 19:55 Athea5130

    ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)

  • 24.09.25 19:56 Athea5130

    ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)

  • 24.09.25 19:56 Athea5130

    ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)

  • 24.09.25 19:56 Athea5130

    ETHICAL BITCOIN HACKER/ BEST WAY RECOVERY BITCOIN I believed I was completely lost. I was unable to withdraw money from my investment wallet after making a dubious investment, and until I discovered Best Way Hacker Company, no one could assist me in unfreezing it. This group handled my matter with attention and urgency. In a matter of days, they were able to retrieve my frozen investment and transfer it to a new wallet that I owned. They restored my hope in a big way. Best Way Hacker restored my money and my peace of mind, and for that I will always be grateful. Email.. [email protected] WhatsApp..+39-(350)-967-(1925)

  • 24.09.25 20:52 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.09.25 20:52 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.09.25 12:29 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider (recoveryfundprovider @ gmail. com WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and i am endlessly grateful.

  • 26.09.25 15:42 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.09.25 15:42 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.09.25 16:40 Slimbella

    I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.

  • 26.09.25 16:40 Slimbella

    I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.

  • 26.09.25 19:08 beverlyalex010

    In 2022, I lost 1.5 ETH in what I thought was a promising Twitter investment. I reached out to the so-called brokers behind it, but they vanished and stopped replying. For years, I carried the heavy belief that my crypto was gone forever. Then, by chance, I discovered RecoveryFundProvider ( [email protected]. WhatsApp +44 736-644-5035) through a finance podcast. That moment changed everything. Their team didn’t lure me in with false promises or flashy guarantees. Instead, they explained their process clearly specializing in advanced blockchain tracing, smart contract forensics, and even transaction reversal in certain cases. Skeptical but hopeful, I allowed them to review my case. What followed was beyond my expectations. They dug deep into the blockchain ledger, followed the coin’s complex movements across multiple addresses, and even collaborated with global nodes to trace every trail. Two weeks later, I received an alert I never thought I’d see again: my crypto had been fully recovered and safely transferred back to me. I cried tears of relief. What sets RecoveryFundProvider apart isn’t just their cutting-edge expertise, but their unwavering ethics and dedication. They treat every client like more than just another case number even years after a loss. Today, I can confidently say they live up to their name, and i am endlessly grateful.

  • 26.09.25 19:53 carolinehudso83

    You are one step away from recovering your lost crypto funds. CAPITAL REDEMPTION WIZARD is the solution. Without them, I would have lost everything. I was scammed through a compromised email, lured by a fake Elon Musk Bitcoin investment. After applying and completing KYC, I was credited with 2.5 Bitcoin. When I tried to withdraw, I was hit with fees, and my wallet was emptied of $103,000.00. Their support team was hostile. I researched and found CAPITAL REDEMPTION WIZARD. They recovered my hacked Bitcoin. I learned the Bitcoin offer was a scam. CAPITAL REDEMPTION WIZARD guided me through this. Email: ( [email protected] ) Whats app or text +1 518 468 2985 Website https://bestrecoveryagent.com/

  • 26.09.25 22:25 Slimbella

    I fully recommend Sylvester Bryant. He recovered €230,000 in Ethereum for me after I believed it was lost for good. His talent for tracing and reclaiming funds stolen by scammers impresses me deeply. I valued his calm, skilled approach and solid grasp of technology. This gained my confidence at every turn. If scammers have stolen your cash, contact him now. Reach out by email at yt7cracker@gmail. com or via WhatsApp at +1 512 577 7957. He dedicates himself to helping people recover their belongings. His support changed everything for me.

  • 26.09.25 22:59 elizabethrush89

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  • 26.09.25 22:59 elizabethrush89

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  • 27.09.25 03:07 Angela_Moore

    I thought my money was lost forever. Then Mr. Sylvester stepped in. He tracked down and recovered $107,000 in stablecoins , plus all my earnings. His talent for finding scam-stolen funds left me stunned. I loved how he handled everything with real expertise and solid tech skills. It got my scammed cash back safe. I trusted him completely. If you've lost funds to a scam, reach out to him now. Email [email protected] or text on WhatsApp at +1 512 577 7957. His support saved me.

  • 28.09.25 00:42 Anitastar

    Wizard Hilton Cyber Tech's strategic approach to Bitcoin recovery represents a mutually beneficial collaboration that offers valuable advantages for all involved. At the core of this innovative partnership is a shared commitment to leveraging cutting-edge technology and expertise to tackle the increasingly complex challenges of cryptocurrency theft and loss. By combining Wizard Hilton's world-class cybersecurity capabilities with the deep industry insights and recovery methodologies of Cyber Tech, this alliance is poised to revolutionize the way individuals and organizations safeguard their digital assets. Through a meticulous, multi-layered process, the team meticulously analyzes each case, employing advanced forensic techniques to trace the flow of stolen funds and identify potential recovery avenues. This rigorous approach not only maximizes the chances of successful Bitcoin retrieval, but also provides invaluable intelligence to enhance future security measures and prevention strategies. Importantly, the collaboration is built on a foundation of trust, transparency, and a genuine concern for the well-being of clients, ensuring that the recovery process is handled with the utmost care and discretion. As the cryptocurrency landscape continues to evolve, this strategic alliance between Wizard Hilton Cyber Tech stands as a shining example of how industry leaders can come together to safeguard digital assets, protect victims of cybercrime, and pave the way for a more secure and resilient cryptocurrency ecosystem. Email : wizardhiltoncybertech ( @ ) gmail (. ) com     OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number  +18737715701 Thanks.

  • 28.09.25 01:48 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 28.09.25 01:48 marcushenderson624

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  • 28.09.25 01:49 marcushenderson624

    Bitcoin Recovery Testimonial After falling victim to a cryptocurrency scam group, I lost $354,000 worth of USDT. I thought all hope was lost from the experience of losing my hard-earned money to scammers. I was devastated and believed there was no way to recover my funds. Fortunately, I started searching for help to recover my stolen funds and I came across a lot of testimonials online about Capital Crypto Recovery, an agent who helps in recovery of lost bitcoin funds, I contacted Capital Crypto Recover Service, and with their expertise, they successfully traced and recovered my stolen assets. Their team was professional, kept me updated throughout the process, and demonstrated a deep understanding of blockchain transactions and recovery protocols. They are trusted and very reliable with a 100% successful rate record Recovery bitcoin, I’m grateful for their help and highly recommend their services to anyone seeking assistance with lost crypto. Contact: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Email: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 13:47 thomassankara

    USDT recovery expert / company I thought my money was lost forever. Then Mr. Sylvester stepped in. He tracked down and recovered $107,000 in stablecoins , plus all my earnings. His talent for finding scam-stolen funds left me stunned. I loved how he handled everything with real expertise and solid tech skills. It got my scammed cash back safe. I trusted him completely. If you've lost funds to a scam, reach out to him now. Email [email protected] or text on WhatsApp at +1 512 577 7957. His support saved me.

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